SOME SUMMATION FORMULAS FOR THE HYPERGEOMETRIC SERIES r+2Fr+1(1/2)

The aim of this paper is to obtain explicit expressions of the generalized hypergeometric function r+2Fr+1. [ a, b,. 1/ 2 (a + b + j + 1), (fr + mr). (fr) ; 1. 2. ] for j = 0, ±1,..., ±5,, where r pairs of numeratorial and denominatorial parameters differ by positive integers mr. The results are derived with the help of an expansion in terms of a finite sum of 2F1( 1/ 2 ) functions and a generalization of Gauss second summation theorem due to Lavoie et al. [J. Comput. Appl. Math. 72, 293-300 (1996)]. Some special and limiting cases are also given.